The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
Hoge,A presentation of the trace algebra of three3×3matrices,Journal of Algebra358 (2012) 257–268
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Fermionic trace relations and supersymmetric indices at finite $N$
The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.